The initial value problem for the equations of motion of viscous and heat-conductive gases
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Publication:1137917
DOI10.1215/kjm/1250522322zbMath0429.76040OpenAlexW1569509154MaRDI QIDQ1137917
Akitaka Matsumura, Takaaki Nishida
Publication date: 1980
Published in: Journal of Mathematics of Kyoto University (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1215/kjm/1250522322
initial value problemequations of motionexistence and uniquenessglobal solutions in timeideal, polytropic, compressible, viscous and heat-conductive
Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Gas dynamics (general theory) (76N15) Partial differential equations of mixed type and mixed-type systems of partial differential equations (35M99)
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compressible Navier Stokes equations ⋮ Global well-posedness of the Cauchy problem of two-dimensional compressible Navier-Stokes equations in weighted spaces ⋮ A theorem of global existence of solutions to nonlinear wave equations in four space dimensions ⋮ Unnamed Item ⋮ Asymptotic behavior of solutions of the compressible Navier-Stokes equations on the half-space ⋮ Existence of a classical solution to complex material flow problems ⋮ Global well-posedness for the viscous shallow water system with Korteweg type ⋮ The decay rate of solution for the bipolar Navier-Stokes-Poisson system ⋮ On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas ⋮ Time decay rates for the compressible viscoelastic flows ⋮ Unnamed Item ⋮ Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid ⋮ Global existence and the optimal decay rates for the three dimensional compressible nematic liquid crystal flow ⋮ On self-similar solutions to degenerate compressible Navier-Stokes equations ⋮ On free boundary problem for compressible Navier-Stokes equations with temperature-dependent heat conductivity ⋮ Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas ⋮ Compressible Navier-Stokes system: large solutions and incompressible limit ⋮ Optimal decay rate for the compressible Navier-Stokes-Poisson system in the critical \(L^p\) framework ⋮ Stability of non-constant equilibrium solutions for two-fluid non-isentropic Euler-Maxwell systems arising in plasmas ⋮ Dynamical behaviors of the solution to a periodic initial-boundary value problem of the generalized Rosenau-RLW-Burgers equation ⋮ Large-time behavior of solutions in the critical spaces for the non-isentropic compressible Navier-Stokes equations with capillarity ⋮ Asymptotic stability of planar rarefaction waves under periodic perturbations for 3-d Navier-Stokes equations ⋮ Global classical solutions to the 2D compressible Navier-Stokes equations with vacuum ⋮ Wave propagation for the compressible Navier–Stokes equations ⋮ Incompressible hydrodynamic approximation with viscous heating to the Boltzmann equation ⋮ Global stability of combination of viscous contact wave with rarefaction wave for compressible Navier–Stokes equations with temperature-dependent viscosity ⋮ On regular solutions to compressible radiation hydrodynamic equations with far field vacuum ⋮ Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations ⋮ Local exact controllability for the two- and three-dimensional compressible Navier–Stokes equations ⋮ Blow up criteria for the 2D compressible Navier-Stokes equations in bounded domains with vacuum ⋮ Global Solutions to the Three-Dimensional Full Compressible Navier--Stokes Equations with Vacuum at Infinity in Some Classes of Large Data ⋮ Global classical solutions to the 3D isentropic compressible Navier–Stokes equations in a bounded domain ⋮ The sharp time-decay rates for one-dimensional compressible isentropic Navier-Stokes and magnetohydrodynamic flows ⋮ The Rayleigh-Bénard problem for compressible fluid flows ⋮ Optimal decay rates for the compressible fluid models of Korteweg type ⋮ Vanishing viscosity limit of the three-dimensional barotropic compressible Navier-Stokes equations with degenerate viscosities and far-field vacuum ⋮ Anisotropy and stratification effects in the dynamics of fast rotating compressible fluids ⋮ Partially dissipative systems in the critical regularity setting, and strong relaxation limit ⋮ Entropy-bounded solutions to the 3D compressible heat-conducting magnetohydrodynamic equations with vacuum at infinity ⋮ Asymptotic stability of the stationary solution to an outflow problem for the compressible Navier-Stokes equations for a reacting mixture ⋮ Global classical solutions for partially dissipative hyperbolic system of balance laws ⋮ Existence and nonlinear stability of stationary solutions to the full compressible Navier-Stokes-Korteweg system ⋮ Blow-up criterions of strong solutions to 3D compressible Navier-Stokes equations with vacuum ⋮ On the global solvability and the non-resistive limit of the one-dimensional compressible heat-conductive MHD equations ⋮ Global existence and decay of strong solutions to the compressible Navier-Stokes-Poisson equations in bounded domains ⋮ Green’s function and pointwise convergence for compressible Navier-Stokes equations ⋮ Blowup of smooth solution for non-isentropic magnetohydrodynamic equations without heat conductivity ⋮ Compressible Navier-Stokes approximation to the Boltzmann equation ⋮ Local existence of solution for the initial boundary value problem of fully nonlinear wave equation ⋮ On the existence of a solution for a model of stem cell differentiation ⋮ Stability and instability of steady-state solutions for a hydrodynamic model of semiconductors ⋮ Optimal decay rates of the compressible fluid models of Korteweg type ⋮ Weak solutions of the Navier-Stokes equations for compressible flows in a half-space with no-slip boundary conditions ⋮ A regularity criterion for the weak solutions to the Navier-Stokes-Fourier system ⋮ The initial value problem for a multi-dimensional radiation hydrodynamics model with viscosity ⋮ Global well-posedness and large time behaviour of the viscous liquid-gas two-phase flow model in ℝ3 ⋮ Decay rates of the compressible Hall-magnetohydrodynamic model for quantum plasmas ⋮ Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid ⋮ Particle hydrodynamic moment models in biology and microelectronics: Singular relaxation limits ⋮ LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES ⋮ Low Mach number limit of the full Navier-Stokes equations ⋮ Blow-up of viscous heat-conducting compressible flows ⋮ On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities ⋮ Global existence and asymptotic behavior for a multidimensional nonisentropic hydrodynamic semiconductor model with the heat source ⋮ Nonlinear stability of rarefaction waves for the compressible Navier-Stokes equations with large initial perturbation ⋮ Matrix methods for wave equations ⋮ Large-time behavior of solutions to the Stokes approximation equations for two-dimensional compressible flows ⋮ Local well-posedness in critical spaces for the compressible MHD equations ⋮ Global existence and optimal decay rate of the compressible bipolar Navier-Stokes-Poisson equations with external force ⋮ One new blowup criterion for the 2D full compressible Navier-Stokes system ⋮ Existence and stability of time periodic solution to the compressible Navier-Stokes equation for time periodic external force with symmetry ⋮ Time periodic solutions of the non-isentropic compressible fluid models of Korteweg type ⋮ Stability of the stationary solution of the Cauchy problem to a semiconductor full hydrodynamic model with recombination-generation rate ⋮ Strong solutions to compressible barotropic viscoelastic flow with vacuum ⋮ Time decay rates for the equations of the compressible heat-conductive flow through porous media ⋮ EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS FOR A COMPRESSIBLE MULTIPHASE NAVIER–STOKES MISCIBLE FLUID-FLOW PROBLEM IN DIMENSION n = 1 ⋮ Existence of global weak solutions for 3D degenerate compressible Navier-Stokes equations ⋮ Spectral analysis of linearized stationary equations of viscous compressible fluid in $\mathbb {R}^3$, with periodic boundary conditions ⋮ Long-Term Regularity of Two-Dimensional Navier--Stokes--Poisson Equations ⋮ Refined pointwise estimates for the Navier–Stokes–Poisson equations ⋮ Compressible Navier–Stokes Equations with hyperbolic heat conduction ⋮ The optimal time decay rates for incompressible viscoelastic fluids in critical framework ⋮ Stability on large non-constant steady states of semiconductor equations ⋮ Existence and uniqueness of small energy weak solution to multi-dimensional compressible Navier-Stokes equations with large external potential force ⋮ Decay of the 3D viscous liquid-gas two-phase flow model with damping ⋮ Global Classical Solutions and Large-Time Behavior of the Two-Phase Fluid Model ⋮ A Generalized Poisson--Nernst--Planck--Navier--Stokes Model on the Fluid with the Crowded Charged Particles: Derivation and Its Well-Posedness ⋮ Global solutions for coupled Kuramoto-Sivashinsky-KdV system ⋮ LOCAL STRONG SOLUTION TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC FLOW WITH LARGE DATA ⋮ The Cauchy problem for viscous shallow water equations ⋮ GLOBAL CLASSICAL SOLUTIONS FOR A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL ⋮ About Compressible Viscous Fluid Flow in a 2-dimensional Exterior Domain ⋮ Remark on stability of rarefaction waves to the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefficient ⋮ Global existence of ideal invicid compressible and heat-conductive fluids with radial symmetry ⋮ Stability and large-time behavior of the inviscid Boussinesq system for the micropolar fluid with damping ⋮ Optimal large-time behavior of the full 3D compressible MHD system ⋮ On the global existence and time-decay rates for a parabolic–hyperbolic model arising from chemotaxis ⋮ Global solutions to the 3D compressible Navier–Stokes equations with a class of special initial data ⋮ On stationary convective motion of viscous compressible and heat-conductive fluid ⋮ Local Strong Solutions to the Full Compressible Navier--Stokes System with Temperature-Dependent Viscosity and Heat Conductivity ⋮ Linear Stability of the Couette Flow in the 3D Isentropic Compressible Navier--Stokes Equations ⋮ Well-posedness and exponential decay for the Navier–Stokes equations of viscous compressible heat-conductive fluids with vacuum ⋮ Global existence and decay estimates of solutions to the MHD–Boussinesq system with stratification effects* ⋮ OPTIMAL CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH POTENTIAL FORCES ⋮ Low Mach number limit for viscous compressible flows ⋮ On the Cauchy problem of the full Navier-Stokes equations for three-dimensional compressible viscous heat-conducting flows subject to large external potential forces ⋮ Global Well-Posedness of Classical Solutions to the Cauchy Problem of Two-Dimensional Barotropic Compressible Navier--Stokes System with Vacuum and Large Initial Data ⋮ Asymptotic stability of solutions to the Navier–Stokes–Fourier system driven by inhomogeneous Dirichlet boundary conditions ⋮ Global Existence of Weak Solutions to the Compressible Navier--Stokes Equations with Temperature-Depending Viscosity Coefficients ⋮ Global in time existence of small solutions of non‐linear thermoviscoelastic equations ⋮ Global strong solutions to the 3D non-isentropic compressible Navier-Stokes-Poisson equations in bounded domains ⋮ The Cauchy Problem for the \(\boldsymbol{N}\)-Dimensional Compressible Navier–Stokes Equations without Heat Conductivity ⋮ Immediate Blowup of Entropy-Bounded Classical Solutions to the Vacuum Free Boundary Problem of Nonisentropic Compressible Navier–Stokes Equations ⋮ Global Regular Solutions for one-dimensional Degenerate Compressible Navier--Stokes Equations with Large Data and Far Field Vacuum ⋮ Global Existence Versus Blow-Up for Multidimensional Hyperbolized Compressible Navier–Stokes Equations ⋮ Local and global well-posedness of entropy-bounded solutions to the compressible Navier-Stokes equations in multi-dimensions ⋮ Global well-posedness of the 1d compressible Navier-Stokes system with rough data ⋮ Critical regularity issues for the compressible Navier-Stokes system in bounded domains ⋮ Green's function and pointwise estimate for a generalized Poisson‐Nernst‐Planck‐Navier‐Stokes model in dimension three ⋮ The existence results for a new 2‐D compressible fluid model with the horizontal thermal gradient effect ⋮ Global classical solutions to the compressible Navier–Stokes equations with Navier-type slip boundary condition in 2D bounded domains ⋮ The optimal convergence rates for the multi-dimensional compressible viscoelastic flows ⋮ Global strong solutions of 3D compressible isothermal magnetohydrodynamics ⋮ Global smooth solutions of 3‐D Navier‐Stokes‐Korteweg equations with large initial data ⋮ The Cauchy problem for a quasilinear system of equations with coupling in the linearization ⋮ Global well‐posedness and asymptotics of full compressible non‐resistive magnetohydrodynamics system with large external potential forces ⋮ Space-time decay rates for the 3D full compressible MHD equations ⋮ Some existence results for the Brinkman-Fourier system ⋮ Cavity Dynamics and Regularity for Compressible Navier–Stokes Equations ⋮ Large-time behavior of global solutions to the Cauchy problem of one-dimensional viscous and heat-conducting ionized gas ⋮ Global existence and large time behavior for the 2-D compressible Navier-Stokes equations without heat conductivity ⋮ Compressible Navier‐Stokes equations with ripped density ⋮ Solving the non-isentropic Navier-Stokes equations in odd space dimensions: The Green function method ⋮ Global classical solutions to the 3D Navier–Stokes–Korteweg equations with small initial energy ⋮ Global large solutions to planar magnetohydrodynamics equations with temperature-dependent coefficients ⋮ Existence and asymptotic stability of stationary waves for symmetric hyperbolic–parabolic systems in half-line ⋮ Decay of the compressible magneto-micropolar fluids ⋮ On the non-resistive limit and the magnetic boundary-layer for one-dimensional compressible magnetohydrodynamics ⋮ Singularity formation of the compressible non-barotropic flows with zero heat conductivity ⋮ Mathematical modeling and qualitative analysis of viscoelastic conductive fluids ⋮ The large-time behavior of solutions in the critical L p framework for compressible viscous and heat-conductive gas flows ⋮ The unique global solvability and optimal time decay rates for a multi-dimensional compressible generic two-fluid model with capillarity effects * ⋮ Optimal Large-Time Behavior of the Two-Phase Fluid Model in the Whole Space ⋮ Local Existence and Uniqueness of Strong Solutions to the Free Boundary Problem of the Full Compressible Navier--Stokes Equations in three dimensions ⋮ Weak Serrin‐type criterion for the three‐dimensional viscous compressible Navier–Stokes system ⋮ A blow-up criterion for compressible viscous heat-conductive flows ⋮ Local strong solutions to the stochastic compressible Navier–Stokes system ⋮ Decay of Dissipative Equations and Negative Sobolev Spaces ⋮ Backward self-similar solutions for compressible Navier–Stokes equations ⋮ Global Well-Posedness and Decay Rates of Strong Solutions to a $P1$-Approximation Model Arising in Radiation Hydrodynamics ⋮ Compressible Navier-Stokes approximation for the Boltzmann equation in bounded domains ⋮ On one-dimensional compressible Navier-Stokes equations with degenerate viscosity and constant state at far fields ⋮ Blow-up of smooth solutions to the isentropic compressible MHD equations ⋮ Existence of solutions for compressible fluid models of Korteweg type ⋮ Strong Solutions to the Compressible Navier--Stokes--Vlasov--Fokker--Planck Equations: Global Existence Near the Equilibrium and Large Time Behavior ⋮ Global existence of classical solutions to two‐dimensional Navier–Stokes equations with Cauchy data containing vacuum ⋮ Stability of non‐constant steady‐state solutions for non‐isentropic Euler–Maxwell system with a temperature damping term ⋮ Strong solutions to 3D compressible magnetohydrodynamic equations with Navier‐slip condition ⋮ FREE-BOUNDARY PROBLEM OF THE ONE-DIMENSIONAL EQUATIONS FOR A VISCOUS AND HEAT-CONDUCTIVE GASEOUS FLOW UNDER THE SELF-GRAVITATION ⋮ Global strong spherically symmetric solutions to the full compressible Navier-Stokes equations with stress free boundary ⋮ Decay Rates for a Nonconservative Compressible Generic Two-Fluid Model ⋮ Système d'équations d'un gaz visqueux modélisant l'atmosphère avec la force de Coriolis et la stabilité de l'état d'équilibre ⋮ Global Solutions to the Isentropic Compressible Navier--Stokes Equations with a Class of Large Initial Data ⋮ Global existence and well-posedness of the 2D viscous shallow water system in Sobolev spaces with low regularity ⋮ Global existence and temporal decay for the 3D compressible Hall-magnetohydrodynamic system ⋮ Local existence of strong solutions and weak–strong uniqueness for the compressible Navier–Stokes system on moving domains ⋮ On an initial boundary value problem for gas dynamics in thermal nonequilibrium ⋮ Global existence and asymptotic behavior for the 3D compressible magneto-micropolar fluids in a bounded domain ⋮ Unnamed Item ⋮ Existence of strong solutions to the rotating shallow water equations with degenerate viscosities ⋮ The self-similar solutions to full compressible Navier–Stokes equations without heat conductivity ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Asymptotic stability of stationary solutions to the compressible bipolar Navier–Stokes–Poisson equations ⋮ The large time behavior of the free boundary for one dimensional compressible Navier-Stokes equations ⋮ LOCAL SOLVABILITY OF AN INITIAL BOUNDARY VALUE PROBLEM FOR A QUASILINEAR HYPERBOLIC-PARABOLIC SYSTEM ⋮ VACUUM STATE FOR SPHERICALLY SYMMETRIC SOLUTIONS OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS ⋮ Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation* ⋮ Global Well-Posedness of the One-Dimensional Compressible Navier--Stokes Equations with Constant Heat Conductivity and Nonnegative Density ⋮ On the existence of local classical solutions to the Navier-Stokes equations with degenerate viscosities ⋮ The large-time behavior of the multi-dimensional hyperbolic-parabolic model arising from chemotaxis ⋮ Optimal time‐decay rates for the 3D compressible Magnetohydrodynamic flows with discontinuous initial data and large oscillations ⋮ Unnamed Item ⋮ Global classical solution to the 3D isentropic compressible Navier-Stokes equations with general initial data and a density-dependent viscosity coefficient ⋮ Optimal time decay of the compressible Navier–Stokes equations for a reacting mixture ⋮ Dissipative Reactive Fluid Models from the Kinetic Theory ⋮ Well-posedness for the viscous rotating shallow water equations with friction terms ⋮ Global existence of weak solution to Navier–Stokes equations with large external force and general pressure ⋮ Exponential decay for Lions-Feireisl's weak solutions to the barotropic compressible Navier-Stokes equations in 3D bounded domains ⋮ Global solutions of compressible barotropic Navier–Stokes equations with a density-dependent viscosity coefficient ⋮ On the Global Motion of Viscous Compressible Barotropic Flows Subject to Large External Potential Forces and Vacuum ⋮ Global well-posedness of non-heat conductive compressible Navier–Stokes equations in 1D ⋮ On temporal decay estimates for the compressible nematic liquid crystal flow in ⋮ Incompressible limit for compressible viscoelastic flows with large velocity ⋮ The compressible Navier-Stokes equations with slip boundary conditions of friction type ⋮ Global well-posedness of compressible magneto-micropolar fluid equations ⋮ Global strong solutions of 3D compressible Navier-Stokes equations with short pulse type initial data ⋮ Linear instability analysis on compressible Navier-Stokes equations with strong boundary layer ⋮ The initial value problem for the equations of motion of fractional compressible viscous fluids ⋮ The global classical solution to compressible system with fractional viscous term ⋮ Global Regularity for a Radiation Hydrodynamics Model with Viscosity and Thermal Conductivity ⋮ Space-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction ⋮ Optimal temporal decay rates for the compressible viscoelastic flows ⋮ Global existence and optimal decay rates for a generic non-conservative compressible two-fluid model ⋮ Global well-posedness and large-time behavior for the equilibrium diffusion model in radiation hydrodynamics ⋮ The regularity and uniqueness of a global solution to the isentropic Navier-Stokes equation with rough initial data ⋮ Global wellposedness of the 3D compressible Navier–Stokes equations with free surface in the maximal regularity class ⋮ Global solutions to the 2D compressible Navier-Stokes equations with some large initial data ⋮ Global Stability and Nonvanishing Vacuum States of 3D Compressible Navier–Stokes Equations ⋮ Propagation of Rough Initial Data for Navier–Stokes Equation ⋮ On the Half-Space or Exterior Problems of the 3D Compressible Elastic Navier–Stokes–Poisson Equations ⋮ Decay of the compressible Navier-Stokes equations with hyperbolic heat conduction ⋮ Regularity and uniqueness of global solutions for the 3D compressible micropolar fluids ⋮ Time decay of solutions for compressible isentropic non-Newtonian fluids ⋮ Global solutions of 3D isentropic compressible Navier-Stokes equations with two slow variables ⋮ The existence of a weak solution for a compressible multicomponent fluid structure interaction problem ⋮ Decay of the Compressible Navier-Stokes Equations with Hyperbolic Heat Conduction ⋮ Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment ⋮ The Cauchy problem for the nonisentropic compressible MHD fluids: Optimal time‐decay rates ⋮ Some Serrin type blow‐up criteria for the three‐dimensional viscous compressible flows with large external potential force ⋮ Optimal decay rate of solutions to the two‐phase flow model ⋮ Global strong solutions to full compressible magnetohydrodynamic system with vacuum in 3D exterior domains ⋮ On the vanishing elastic limit of compressible liquid crystal material flow ⋮ The optimal decay rates of classical solutions to the 3D compressible Navier‐Stokes equations ⋮ Optimal decay rate and convergence of the incompressible viscous resistive MHD system ⋮ Global solutions for two-dimensional viscous pressureless flows with large variations of density ⋮ Large time behavior of solutions to a diffusion approximation radiation hydrodynamics model ⋮ Partial dissipation and sub-shock ⋮ Global existence and time behaviour of strong solution to a compressible non-Newtonian fluid ⋮ Global classical solutions to the viscous two-phase flow model with slip boundary conditions in 3D exterior domains ⋮ Optimal large time behavior of the full compressible Navier-Stokes system in \(\mathbb{R}^3\) ⋮ Asymptotic stability of a nonlinear wave for an outflow problem of the bipolar Navier-Stokes-Poisson system under large initial perturbation ⋮ A new blow-up criterion for the 2D full compressible Navier-Stokes equations without heat conduction in a bounded domain ⋮ Global classical solutions to the compressible micropolar viscous fluids with large oscillations and vacuum ⋮ On the regularity criteria for the three‐dimensional compressible Navier–Stokes system in Lorentz spaces ⋮ Global existence of strong solutions to the 3D isentropic compressible Navier–Stokes equations with density‐dependent viscosities ⋮ Optimality of the decay estimate of solutions to the linearised curl-free compressible Navier-Stokes equations ⋮ Local well-posedness of the 1d compressible Navier-Stokes system with rough data ⋮ Existence and exponential growth of global classical solutions to the compressible Navier-Stokes equations with slip boundary conditions in 3D bounded domains ⋮ Well-posedness for the one-dimensional inviscid Cattaneo-Christov system ⋮ Global existence for a class of large solution to compressible Navier-Stokes equations with vacuum ⋮ Large time behavior of solutions to a reduced gravity two and a half layer model with damping ⋮ Nonuniform dependence on initial data for the 2D viscous shallow water equations ⋮ Pointwise space-time estimates of two-phase fluid model in dimension three ⋮ Global existence and decay estimates of the classical solution to the compressible Navier-Stokes-Smoluchowski equations in \(\mathbb{R}^3\) ⋮ Optimal temporal decay rate of the non‐isentropic compressible Navier–Stokes–Poisson system ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Helically symmetric solutions to the 3D Navier-Stokes equations for compressible isentropic fluids ⋮ The solvability of the initial boundary-value problem for equations of motion of a viscous compressible barotropic liquid in the spaces \(W_ 2^{2+\ell,1+\ell/2}(Q_ T)\) ⋮ An existence theorem for compressible viscous fluids ⋮ Refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure ⋮ The equation of potential flows of a compressible viscous fluid at small Reynolds numbers: Existence, uniqueness, and stabilization of solutions ⋮ Decay rates of the compressible Hall-MHD equations for quantum plasmas ⋮ Existence and uniqueness of stationary solutions for a viscous compressible heat-conducting fluid with large potential and small nonpotential external forces ⋮ Decay rates of higher-order norms of solutions to the Navier-Stokes-Landau-Lifshitz system ⋮ Navier-Stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case ⋮ About the resolvent of an operator from fluid dynamics ⋮ On global motion of a compressible viscous heat-conducting fluid bounded by a free surface ⋮ Compressible viscous flows in a symmetric domain with complete slip boundary: the nonlinear stability of uniformly rotating states with small angular velocities ⋮ Asymptotic behavior of solutions to an electromagnetic fluid model ⋮ Optimal time decay of Navier-Stokes equations with low regularity initial data ⋮ Existence of global solutions for 2-dimensional viscous compressible flows ⋮ On global solutions of Cauchy problems for compressible Navier-Stokes equations ⋮ Nonlinear stability of rarefaction waves for the compressible Navier-Stokes equations with zero heat conductivity ⋮ Convergence to diffusion waves of solutions for viscous conservation laws ⋮ Global classical solutions of compressible isentropic Navier-Stokes equations with small density ⋮ Global solutions to compressible Navier-Stokes equations with spherical symmetry and free boundary ⋮ Global analysis for strong solutions to the equations of a ferrofluid flow model ⋮ Global existence of the solution of nonlinear Schrödinger equations in exterior domains ⋮ Global well-posedness of the 3D non-isothermal compressible fluid model of Korteweg type ⋮ Volume viscosity and internal energy relaxation: error estimates ⋮ Blowup analysis for two-dimensional viscous compressible, heat-conductive Navier-Stokes equations ⋮ Existence results for viscous polytropic fluids with vacuum ⋮ Existence and uniqueness for viscous steady compressible motions ⋮ Well-posedness of a quasistationary model of a viscous compressible fluid ⋮ Existence of global solutions for nonlinear magnetohydrodynamics with finite Larmor radius corrections ⋮ The evolution compressible Navier-Stokes system on polygonal domains ⋮ Convergence to equilibria and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows with large data ⋮ Asymptotic stability of solutions for 1-D compressible Navier-Stokes-Cahn-Hilliard system ⋮ The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball. II: 3D Navier-Stokes equations ⋮ Pointwise estimates for bipolar compressible Navier-Stokes-Poisson system in dimension three ⋮ Axisymmetric solutions of the 3D Navier-Stokes equations for compressible isentropic fluids ⋮ On the stationary solutions of the full compressible Navier-Stokes equations and its stability with respect to initial disturbance ⋮ On the local energy decay of higher derivatives of solutions for the equations of motion of compressible viscous and heat-conductive gases in an exterior domain in \(\mathbb{R}^3\) ⋮ Global existence and large-time behavior of smooth solutions to the Timoshenko-Fourier system in thermoelasticity ⋮ On hyperbolic-dissipative systems of composite type ⋮ Decay rates of solutions to a P1-approximation model arising from radiation hydrodynamics ⋮ Global solution to 3D spherically symmetric compressible Navier-Stokes equations with large data ⋮ Long-time behavior of solution to the compressible micropolar fluids with external force ⋮ Global existence of weak solution to the free boundary problem for compressible Navier-Stokes ⋮ Global existence and semiclassical limit for quantum hydrodynamic equations with viscosity and heat conduction ⋮ Global existence and well-posedness of the 2D viscous shallow water system in Besov spaces ⋮ The Cauchy problem for compressible Navier-Stokes equations with shear viscosity and large data ⋮ Asymptotics of solutions of nonlinear parabolic equations. ⋮ The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids ⋮ Blowup criteria for strong solutions to the compressible Navier-Stokes equations with variable viscosity ⋮ Global solutions to nonisentropic hydrodynamic models for two-carrier plasmas ⋮ On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation ⋮ The zero Mach number limit of the three-dimensional compressible viscous magnetohydrodynamic equations ⋮ Global weak solutions to the full compressible Navier-Stokes equations with spherically symmetric data in a 2-D ball ⋮ Serrin-type blowup criterion for full compressible Navier-Stokes-Maxwell system with vacuum ⋮ On the initial boundary-value problem for viscous heat conducting compressible fluids ⋮ On global solutions to the initial-boundary value problem for the damped nonlinear Schrödinger equations ⋮ Local existence of the strong solutions for the full Navier-Stokes-Poisson equations ⋮ Unique solvability of the initial boundary value problems for compressible viscous fluids. ⋮ On the Cauchy problem for the Boltzmann equation in the whole space: Global existence and uniform stability in \(L_{\xi}^{2}(H_{x}^{N})\) ⋮ Behaviour of the Fokker-Planck-Boltzmann equation near a Maxwellian ⋮ Global weak solvability to the regularized viscous compressible heat conductive flow ⋮ Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas ⋮ Global solution to the viscous compressible barotropic multipolar gas ⋮ Pointwise estimates of solution for the Navier-Stokes-Poisson equations in multi-dimensions ⋮ Simulation of turbulence with the \(k-\epsilon\) model ⋮ Time periodic solutions of compressible Navier-Stokes equations ⋮ Global existence and convergence rates of smooth solutions for the compressible magnetohydrodynamic equations ⋮ Optimal decay rate of the compressible Navier-Stokes-Poisson system in \(\mathbb R^3\) ⋮ Local strong solution to the compressible viscoelastic flow with large data ⋮ Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain ⋮ Strong solution to the compressible magnetohydrodynamic equations with vacuum ⋮ Asymptotic stability of solutions to the nonisentropic hydrodynamic model for semiconductors ⋮ Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations ⋮ Asymptotic behavior of the solution to a nonisentropic hydrodynamic model of semiconductors ⋮ Stability of boundary layer and rarefaction wave to an outflow problem for compressible Navier-Stokes equations under large perturbation ⋮ A note on spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients ⋮ A regularity result for a solid-fluid system associated to the compressible Navier-Stokes equations ⋮ Strong solutions to the three-dimensional compressible viscoelastic fluids ⋮ A note on asymptotic behavior of solutions for the one-dimensional bipolar Euler-Poisson system ⋮ Large-time behavior of solutions to the equations of a viscous polytropic ideal gas ⋮ Global well-posedness and optimal large-time behavior of strong solutions to the non-isentropic particle-fluid flows ⋮ Global well-posedness for systems of hyperbolic-parabolic composite type with center manifold ⋮ Cauchy problem for viscous rotating shallow water equations ⋮ Incompressible limits of the Navier-Stokes equations for all time ⋮ Generalized Huygens' principle for bipolar non-isentropic compressible Navier-Stokes-Poisson system in dimension three ⋮ Optimal decay rates of isentropic compressible Navier-Stokes equations with discontinuous initial data ⋮ Global well-posedness of strong solutions with large oscillations and vacuum to the compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile ⋮ A combination of energy method and spectral analysis for study of equations of gas motion ⋮ Global existence for the Cauchy problem for the viscous shallow water equations ⋮ Large time behavior of the semigroup on \(L^p\) spaces associated with the linearized compressible Navier-Stokes equation in a cylindrical domain ⋮ Stability of steady state solutions for an isentropic hydrodynamic model of semiconductors of two species ⋮ Global solution of the isothermal viscous gas equation in an exterior domain subject to a large potential force ⋮ Existence theorems for compressible viscous fluids having zero shear viscosity ⋮ Large-time regularity of viscous surface waves ⋮ Solutions in the large for certain nonlinear parabolic systems ⋮ On a global in time existence theorem of smooth solutions to a nonlinear wave equation with viscosity ⋮ Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws ⋮ \(L_2\) and \(L_\infty\) estimates of the solutions for the compressible Navier-Stokes equations in a 3D exterior domain ⋮ Some uniform estimates and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows ⋮ On a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain
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